Mathematics of FinanceMCQPYQ Sep 24Question 1483 of 512
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A loan of 16,550\displaystyle 16,550 is to be paid in three equal annual instalments at compound interest. The value of annual instalment, if the rate of interest is 10%\displaystyle 10\% per annum is:

Options

A1,243\displaystyle 1,243
B6,655\displaystyle 6,655
C6,565\displaystyle 6,565
D1,343\displaystyle 1,343
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Correct Answer

Option b6,655\displaystyle 6,655

All Options:

  • A1,243\displaystyle 1,243
  • B6,655\displaystyle 6,655
  • C6,565\displaystyle 6,565
  • D1,343\displaystyle 1,343

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Detailed Solution & Explanation

The present value of an ordinary annuity (loan amount) is: PV=P×[1(1+i)ni]PV = P \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] Given: * Loan amount (PV\displaystyle PV) = 16,550\displaystyle 16,550 * Time (n\displaystyle n) = 3\displaystyle 3 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 First, calculate the annuity factor: Factor=1(1.10)30.10=10.75131480.10=2.48685\text{Factor} = \frac{1 - (1.10)^{-3}}{0.10} = \frac{1 - 0.7513148}{0.10} = 2.48685 Now solve for the annual instalment P\displaystyle P: 16,550=P×2.4868516,550 = P \times 2.48685 P=16,5502.48685=6,655P = \frac{16,550}{2.48685} = 6,655 Thus, the annual instalment is 6,655\displaystyle 6,655. Hence, **Option B** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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